LECTURE 4 Flashcards
(43 cards)
When p=+1, the SD if the portfolio is given by…
And on the graph…
SD(lA+(1-l)B) = lSD(A) + (1-l)SD(B)
Green line between them on return-risk graph
How is the volatile of the portfolio affected by correlation between 2 securities?
Lower correlation = lower volatility
Efficient portfolio means…
Cannot reduce risk without reducing return
Cannot increase return without increasing risk
the efficient frontier AKA
MARKOVITZ FRONTIER
Each point on efficient frontier shows…
A different portfolio with different combo of assets to give a specific risk-return
Explain shape of risk-return ICs
Slope UP - higher risk = need higher return as compensation to keep utility constant.
Higher U to NW where higher return, lower risk.
Risk-return ICs for risk averse investor
STEEPER = more risk averse since for given increase in risk need greater increase in return to compensate.
An investor’s optimal portfolio is given by….
How does this differ by risk preference?
Markovitz frontier tangent to their highest IC.
Risk averse = steeper = tangent at lower risk and lower return.
What kind of assets does Markovitz include?
RISKY assets only.
3 characteristics of risk free assets
- expected return =actual return
- zero variance of return
- covariance riskless and risky = 0
How do weights on risk free asset vary depending on borrowing/lending?
Lending = buy bond, w > 0 Borrowing = sell bond, w < 0
CAL shows…
risk-return trade-off for efficient portfolios that include risky and risk free assets.
Y intercept of CAL
Risk free rate - can get this return without incurring any risk.
Slope of CAL =
E(rA) - rf / sigma A = risk premium (per unit of risk) on risky assets
How do we create the CML?
From Rf up to where CAL and Markowitz intercept, CAL > Markowitz
Then after Markowitz is dominant
How do CAL and CML differ?
CML is a special case of CAL where the risky portfolio = market portfolio
Market portfolio is found where…
What is M?
CML tangent to Markowitz.
This is the most efficient portfolio and includes only risky assets.
Whats the slope at M?
Highest ratio of risk premium to SD at M
SHARPE RATIO of M
Where do we show borrowing and lending @ risk free rate on CML? How does this relate to risk preferences?
Up to M = lending = buy gov bonds = risk averse
After M = borrowing = risk taker
When it is possible to lend/borrow @ risk free rate, an investor is no longer…
restricted to holding a portfolio on markovitz frontier.
2 stages to investor decision
- Estimate Markowitz, CML and find point M
2. Decided how to split investment between M and risk free assets depending on risk preferences.
In reality, how does risk free rate differ by lending and borrowing? How does this affect CML?
Higher rate of borrowing than lending
CML kinked and becomes flatter after M –> new efficient frontier
What does CML NOT tell us?
About INDIVIDUAL SECURITIES - it only talks about efficient portfolios.
CAPM shows…
a linear relationship between expected return of an individual asset that is going to be added to a well-diversified portfolio and its contribution to the portfolio’s risk.
